Question 1

State the Properties of the Normal Curve
-The normal density curve is symmetric about

Accepted Answer

A)  Its mean 
B)  The horizontal axis 
C)  An inflection point 
D)  A point located one standard deviation from the mean 
A)  Its mean 
B)  The horizontal axis 
C)  An inflection point 
D)  A point located one standard deviation from the mean

Question 2

Find the Value of a Normal Random Variable
-A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 450 seconds and a standard deviation of 50 seconds. The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association

Accepted Answer

A)  $386 \mathrm { sec }$ 
B)  $514 \mathrm { sec }$ 
C)  $532.25 \mathrm { sec }$ 
D)  $367.75 \mathrm { sec }$ 
A)  $386 \mathrm { sec }$ 
B)  $514 \mathrm { sec }$ 
C)  $532.25 \mathrm { sec }$ 
D)  $367.75 \mathrm { sec }$

Question 3

Find and Interpret the Area under a Normal Curve
-between $\$ 150,000$ and $\$ 156,300$ if the standard deviation is $\$ 2100$.

Accepted Answer

A)  $49.85 \%$ 
B)  $99.7 \%$ 
C)  $34 \%$ 
D)  $47.5 \%$ 
A)  $49.85 \%$ 
B)  $99.7 \%$ 
C)  $34 \%$ 
D)  $47.5 \%$

Question 4

Provide an appropriate response
-Suppose x is a uniform random variable with c = 10 and d = 90. Find the probability that a randomly selected observation exceeds 26.

Accepted Answer

A)  0.8 
B)  0.2 
C)  0.1 
D)  0.9 
A)  0.8 
B)  0.2 
C)  0.1 
D)  0.9

Question 5

Find the Value of a Normal Random Variable
-A brewery has a beer dispensing machine that dispenses beer into the company s 12 ounce bottles. The distribution for the amount of beer dispensed by the machine follows a normal distribution with a standard deviation of 0.15 ounce. The company can control the mean amount of beer dispensed by the machine. What value of the mean should the company use if it wants to guarantee that 98.5% of the bottles contain at least 12 ounces (the amount on the label)

Accepted Answer

A)  12.325 oz 
B)  12.364 oz 
C)  12.002 oz 
D)  12.001 oz 
A)  12.325 oz 
B)  12.364 oz 
C)  12.002 oz 
D)  12.001 oz

Question 6

Provide an appropriate response
-Suppose x is a uniform random variable with c = 30 and d = 70. Find the probability that a randomly selected observation is between 33 and 65.

Accepted Answer

A)  0.80 
B)  0.20 
C)  0.5 
D)  0.8 
A)  0.80 
B)  0.20 
C)  0.5 
D)  0.8

Question 7

Find and Interpret the Area under a Normal Curve
-The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1300 miles. What is the probability a particular tire of this brand will last longer than 58,700 miles

Accepted Answer

A)  0.8413 
B)  0.1587 
C)  0.2266 
D)  0.7266 
A)  0.8413 
B)  0.1587 
C)  0.2266 
D)  0.7266

Question 8

Find z-scores for a Given Area
-For a standard normal curve, find the z-score that separates the bottom $70 \%$ from the top $30 \%$.

Accepted Answer

A)  $0.53$ 
B)  $0.98$ 
C)  $0.47$ 
D)  $0.12$ 
A)  $0.53$ 
B)  $0.98$ 
C)  $0.47$ 
D)  $0.12$

Question 9

Find and Interpret the Area under a Normal Curve
-less than $\$ 146,600$ if the standard deviation is $\$ 1700$.

Accepted Answer

A)  $2.5 \%$ 
B)  $97.5 \%$ 
C)  $47.5 \%$ 
D)  $95 \%$ 
A)  $2.5 \%$ 
B)  $97.5 \%$ 
C)  $47.5 \%$ 
D)  $95 \%$

Question 10

Find and Interpret the Area under a Normal Curve
-between $\$ 148,200$ and $\$ 151,800$ if the standard deviation is $\$ 1800$.

Accepted Answer

A)  $68 \%$ 
B)  $34 \%$ 
C)  $95 \%$ 
D)  $99.7 \%$ 
A)  $68 \%$ 
B)  $34 \%$ 
C)  $95 \%$ 
D)  $99.7 \%$

Question 11

Find and Interpret the Area under a Normal Curve
-The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a mean of 12.27 ounces and a standard deviation of 0.18 ounce. The cans only hold 12.45 ounces of soda. Every can that has more than 12.45 ounces of soda poured into it causes a spill and the can needs to go through a special cleaning process before it can be sold. What is the probability a randomly selected can will need to go through this process

Accepted Answer

A)  0.1587 
B)  0.3413 
C)  0.8413 
D)  0.6587 
A)  0.1587 
B)  0.3413 
C)  0.8413 
D)  0.6587

Question 12

Find and Interpret the Area under a Normal Curve
-The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2900 miles. What is the probability a certain tire of this brand will last between 53,910 miles and 54,780 miles

Accepted Answer

A)  0.0180 
B)  0.9813 
C)  0.4920 
D)  0.4649 
A)  0.0180 
B)  0.9813 
C)  0.4920 
D)  0.4649

Question 13

Find and Interpret the Area under a Normal Curve
-Use the standard normal distribution to find $\mathrm { P } ( 0 < \mathrm { z } < 2.25 )$.

Accepted Answer

A)  $0.4878$ 
B)  $0.5122$ 
C)  $0.8817$ 
D)  $0.7888$ 
A)  $0.4878$ 
B)  $0.5122$ 
C)  $0.8817$ 
D)  $0.7888$

Question 14

Use Normal Probability Plots to Assess Normality
-A normal probability plot is a graph that plots _____________ versus _____________.

Accepted Answer

A)  observed data, normal scores 
B)  normal score, observed data 
C)  normal data, observed scores 
D)  observed scores, normal data 
A)  observed data, normal scores 
B)  normal score, observed data 
C)  normal data, observed scores 
D)  observed scores, normal data

Question 15

Approximate Binomial Probabilities Using the Normal Distribution
-Assuming that all conditions are met to approximate a binomial probability distribution with the standard normal distribution, then to compute $P ( x \geq 19 )$ from the binomial distribution we must compute _____as the normal approximation.

Accepted Answer

A)  $\mathrm { P } ( \mathrm { x } \geq 18.5 )$ 
B)  $\mathrm { P } ( \mathrm { x } \leq 18.5 )$ 
C)  $\mathrm { P } ( \mathrm { x } \geq 19.1 )$ 
D)  $\mathrm { P } ( \mathrm { x } \leq 18.9 )$ 
A)  $\mathrm { P } ( \mathrm { x } \geq 18.5 )$ 
B)  $\mathrm { P } ( \mathrm { x } \leq 18.5 )$ 
C)  $\mathrm { P } ( \mathrm { x } \geq 19.1 )$ 
D)  $\mathrm { P } ( \mathrm { x } \leq 18.9 )$

Question 16

Provide an appropriate response
-The diameter of ball bearings produced in a manufacturing process can be explained using a uniform distribution over the interval 6.5 to 8.5 millimeters. What is the probability that a randomly selected ball bearing has a diameter greater than 7.4 millimeters

Accepted Answer

A)  0.55 
B)  0.8706 
C)  3.5 
D)  0.4933 
A)  0.55 
B)  0.8706 
C)  3.5 
D)  0.4933

Question 17

Interpret the Area under the Standard Normal Curve as a Probability
-Use the standard normal distribution to find $\mathrm { P } ( - 2.50 < Z < 1.50$ ).

Accepted Answer

A)  $0.9270$ 
B)  $0.8822$ 
C)  $0.6167$ 
D)  $0.5496$ 
A)  $0.9270$ 
B)  $0.8822$ 
C)  $0.6167$ 
D)  $0.5496$

Question 18

Find and Interpret the Area under a Normal Curve
-Use the standard normal distribution to find $\mathrm { P } ( - 2.25 < \mathrm { z } < 0 )$.

Accepted Answer

A)  $0.4878$ 
B)  $0.5122$ 
C)  $0.6831$ 
D)  $0.0122$ 
A)  $0.4878$ 
B)  $0.5122$ 
C)  $0.6831$ 
D)  $0.0122$

Question 19

Find and Interpret the Area under a Normal Curve
-A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 470 seconds and a standard deviation of 40 seconds. Find the probability that a randomly selected boy in secondary school will take longer than 378 seconds to run the mile.

Accepted Answer

A)  0.9893 
B)  0.4893 
C)  0.0107 
D)  0.5107 
A)  0.9893 
B)  0.4893 
C)  0.0107 
D)  0.5107

Question 20

Find the Value of a Normal Random Variable
-A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 440 seconds and a standard deviation of 60 seconds. Between what times do we expect most (approximately 95%) of the boys to run the mile

Accepted Answer

A)  between 322.4 and 557.6 sec 
B)  between 341.3 and 538.736 sec 
C)  between 345 and 535 sec 
D)  between 0 and 538.736 sec 
A)  between 322.4 and 557.6 sec 
B)  between 341.3 and 538.736 sec 
C)  between 345 and 535 sec 
D)  between 0 and 538.736 sec

State the Properties of the Normal Curve -The normal density curve is symmetric about

Find and Interpret the Area under a Normal Curve -between $\$ 150,000$ and $\$ 156,300$ if the standard deviation is $\$ 2100$ .

Provide an appropriate response -Suppose x is a uniform random variable with c = 10 and d = 90. Find the probability that a randomly selected observation exceeds 26.

Provide an appropriate response -Suppose x is a uniform random variable with c = 30 and d = 70. Find the probability that a randomly selected observation is between 33 and 65.

Find z-scores for a Given Area -For a standard normal curve, find the z-score that separates the bottom $70 \%$ from the top $30 \%$ .

Find and Interpret the Area under a Normal Curve -less than $\$ 146,600$ if the standard deviation is $\$ 1700$ .

Find and Interpret the Area under a Normal Curve -between $\$ 148,200$ and $\$ 151,800$ if the standard deviation is $\$ 1800$ .

Find and Interpret the Area under a Normal Curve -Use the standard normal distribution to find $\mathrm { P } ( 0 < \mathrm { z } < 2.25 )$ .

Use Normal Probability Plots to Assess Normality -A normal probability plot is a graph that plots _ versus _.

Provide an appropriate response -The diameter of ball bearings produced in a manufacturing process can be explained using a uniform distribution over the interval 6.5 to 8.5 millimeters. What is the probability that a randomly selected ball bearing has a diameter greater than 7.4 millimeters

Interpret the Area under the Standard Normal Curve as a Probability -Use the standard normal distribution to find $\mathrm { P } ( - 2.50 < Z < 1.50$ ).

Find and Interpret the Area under a Normal Curve -Use the standard normal distribution to find $\mathrm { P } ( - 2.25 < \mathrm { z } < 0 )$ .

Data Collection

Creating Tables and Drawing Pictures of Data

Numerically Summarizing Data

Describing the Relation Between Two Variables

Probability

Discrete Probability Distributions

Sampling Distributions

Estimating the Value of a Parameter Using Confidence Intervals

Hypothesis Tests Regarding a Parameter

Inference on Two Samples

Inference on Categorical Data

Comparing Three or More Means

Inference of the Least-Squares Regression Model and Multiple Regression

Nonparametric Statistics

Filters

Exam 7: The Normal Probability Distribution